Dual-spacecraft game path planning method based on progressive targeting

Abstract

The application relates to a double-spacecraft game path planning method based on a progressive shooting method, which comprises the following steps: establishing a real game optimization model of double-spacecraft under external force dynamics; establishing optimal control conditions of the real game optimization model; based on the optimal control conditions, an optimal solution of a simplified game model of double-spacecraft under no external force dynamics is solved by using a modified shooting method; the optimal solution of the simplified game model is taken as an initial value of the real game optimization model, and the optimal solution of the real game optimization model is solved by using second shooting, so that a real game guidance law of double-spacecraft is obtained. The application solves the problems that the calculation amount of the game guidance law of double-spacecraft is large, and the optimality cannot be guaranteed when the initial value is unreasonable.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerospace guidance and control technology, and in particular to a double-spacecraft game path planning method based on progressive shooting method. BACKGROUND

[0002] With the development of rendezvous and docking technology, especially the non-cooperative rendezvous technology, the use of rendezvous to approach target spacecraft and implement interference or attack has become an important space attack means. Under this situation, how to effectively implement maneuvering to avoid the approach of the enemy spacecraft when the non-cooperative spacecraft attempts to approach our spacecraft has become an important means to protect the safety of our spacecraft.

[0003] The spacecraft rendezvous-anti-rendezvous can be regarded as a double-sided hetero-target optimal control problem, which has more antagonism and conflictivity compared with the classical single-sided optimal control problem. The use of differential game method to dynamically model and plan this type of problem is an effective means to solve this type of problem.

[0004] For the path planning problem of double-spacecraft game orbit, the existing research generally assumes that the two spacecraft have continuous small thrust maneuvering capability, models the spacecraft pursuit-evasion problem as a zero-sum game problem, and then uses the differential game method to study and obtain the equilibrium point (saddle point) of the game problem. This method assumes that the target spacecraft and our spacecraft are "rational people" and have sufficient computing power and logical ability, so as to be able to foresee all possible situations and predict the final benefits, and always adopt the strategy that maximizes their own utility. That is, it is assumed that the target adopts the most advantageous orbit approach guidance law, and then the orbit optimal guidance law of our spacecraft is obtained.

[0005] For the study of spacecraft escape maneuvering, the above method has certain deficiencies in the assumptions of the approach law and control ability of the tracking spacecraft and the rapidity of the generation of the maneuvering guidance law, and cannot meet the needs of future space confrontation. In the direction of the approach law of the tracking spacecraft, the optimality of the escape maneuvering guidance law of the target spacecraft depends on the assumption of the approach strategy and control ability of the tracking spacecraft. If the tracking spacecraft does not use the most advantageous approach, the escape maneuvering guidance law calculated by the differential game method may not be optimal. In terms of the generation of the maneuvering guidance law, the existing calculation of the spacecraft game guidance law is a dense method, which has large amount of calculation and is not suitable for actual on-orbit application. SUMMARY

[0006] To solve the problems of large amount of calculation of the double-spacecraft game guidance law and the inability to guarantee the optimality when the initial value is unreasonable, the present application provides a double-spacecraft game path planning method based on progressive shooting method.

[0007] To achieve the above-mentioned purposes, the technical scheme of the present application is:

[0008] The present application provides a double-spacecraft game path planning method based on progressive shooting method, comprising:

[0009] A real game optimization model of double-spacecraft under external force dynamics is established;

[0010] An optimal control condition of the real game optimization model is established;

[0011] Based on the optimal control condition, a modified shooting method is used to solve the optimal solution of a simplified game model of double-spacecraft under no external force dynamics;

[0012] The optimal solution of the simplified game model is taken as the initial value of the real game optimization model, and the optimal solution of the real game optimization model is solved by using second shooting, so as to obtain the real game guidance law of double-spacecraft.

[0013] Compared with the prior art, the present application has the following beneficial effects:

[0014] According to the scheme of the present application, an efficient game dynamic feedback control law solving algorithm is provided, and efficient solving of double-spacecraft game path is realized through two-step shooting. The specific solving process comprises the following steps: firstly, a simplified game optimization model under no external force dynamics is established, an initial guess with good properties is constructed based on qualitative analysis of the optimal trajectory, and the problem is solved by first shooting. Then, the optimal solution of the no external force dynamics game problem obtained by first shooting is taken as the initial value of the real game problem under external force dynamics, and the final game optimal solution is obtained by second shooting. The initial value is closer to the optimal solution, and the success rate of the shooting method can be improved.

[0015] According to one scheme of the present application, by using the game dynamic feedback control law solving algorithm of twice progressive shooting method, the problems of large calculation amount of double-spacecraft game guidance law in the prior art and the problem that the optimality cannot be guaranteed when the initial value is unreasonable are solved, and an effective solution is provided for double-spacecraft on-orbit game path planning. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical schemes in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0017] Figure 1 The figure schematically shows the implementation flowchart of the double-spacecraft game path planning method based on progressive shooting method provided by the embodiment of the present application.

[0018] Figure 2 schematic diagram illustrating the definition of a double-spacecraft game coordinate system provided by an embodiment of the present application;

[0019] Figure 3 schematic diagram illustrating the solution process of the twice shooting method provided by an embodiment of the present application;

[0020] Figure 4 schematic diagram illustrating the direction of the thrust force provided by an embodiment of the present application;

[0021] Figure 5 schematic diagram illustrating the estimation of the terminal time provided by an embodiment of the present application;

[0022] Figure 6 schematic diagram illustrating the initial direction of the thrust force provided by an embodiment of the present application;

[0023] Figure 7 schematic diagram illustrating the comparison between the guessed trajectory and the optimal trajectory in the first shooting provided by an embodiment of the present application;

[0024] Figure 8 schematic diagram illustrating the comparison between the guessed control and the optimal control in the first shooting provided by an embodiment of the present application;

[0025] Figure 9 schematic diagram illustrating the pursuit-evasion capture game trajectory in the twice shooting provided by an embodiment of the present application;

[0026] Figure 10 schematic diagram illustrating the pursuit-evasion capture game velocity in the twice shooting provided by an embodiment of the present application;

[0027] Figure 11 schematic diagram illustrating the convergence curve in the first shooting provided by an embodiment of the present application;

[0028] Figure 12 schematic diagram illustrating the convergence curve in the second shooting provided by an embodiment of the present application. DETAILED DESCRIPTION

[0029] The description of the embodiments of the present application in this specification should be considered in conjunction with the accompanying drawings, which should be considered part of the complete specification. In the drawings, the shape or thickness of the embodiments can be exaggerated and simplified, or convenient to illustrate. Moreover, the parts of the structures in the drawings will be described separately, and it should be noted that the elements not shown or not described in the drawings are in the form known to those skilled in the art.

[0030] The description of the embodiments herein, any reference to direction or position, is only for the convenience of description, and cannot be understood as any limitation on the scope of protection of the present application. The following description of the preferred embodiments will involve a combination of features, which can exist independently or in combination, and the present application is not particularly limited to the preferred embodiments. The scope of the present application is defined by the claims.

[0031] As shown in Figure 1 , the implementation process of the dual-spacecraft game path planning method based on the progressive shooting method disclosed by the embodiments of the present application specifically includes the following steps:

[0032] Step 100, a real game optimization model of dual-spacecraft under external force dynamics is established.

[0033] Step 200, an optimal control condition of the real game optimization model is established.

[0034] Step 300, based on the optimal control condition, the optimal solution of a simplified game model of dual-spacecraft under no external force dynamics is solved by using the modified shooting method, so as to obtain the optimal control law of the simplified game model, and the optimal control law is used as the initial value of the real game optimization problem.

[0035] Step 400, according to the initial value of the real game optimization problem, the optimal solution of the real game optimization model is solved by using the second shooting, and the real game guidance law of dual-spacecraft is obtained.

[0036] The embodiments use the CW equation to describe the relative dynamics relationship of dual-spacecraft, and specifically describe the implementation process of the dual-spacecraft game path planning method based on the progressive shooting method. As shown in Figure 2 , the origin of the geocentric inertial coordinate system is located at the center of the earth, the X-axis points to the vernal equinox point γ, the Y-axis is perpendicular to the X-axis in the equatorial plane, and the Z-axis is determined by the right-hand rule. The target orbit coordinate system, also known as the Hill coordinate system, has its origin fixed to the center of mass of the target spacecraft, and the x-axis of the orbit coordinate system coincides with the geocentric radius vector r e of the target spacecraft, the z-axis is perpendicular to the orbital plane and points to the momentum direction, and the y-axis is determined by the right-hand rule. The game coordinate system of the embodiments is the Hill coordinate system. The dual-spacecraft includes a tracking spacecraft and an evading spacecraft.

[0037] In the embodiments, as Figure 3The method realizes efficient solution of the actual game path of the two spacecrafts through two-step shooting. The specific solution process includes: first, the game optimization model under the non-external force dynamics is established, the initial guess with good properties is constructed based on the qualitative analysis of the optimal trajectory, and the problem is solved through the first shooting. Then, the optimal solution of the non-external force dynamics simplified game problem obtained by the first shooting is taken as the initial value of the actual or real game problem under the external CW dynamics, and the second shooting is performed to obtain the final game optimal solution. Based on the motion state inversion target control law and control ability of the tracking and escaping spacecrafts, the calculation amount of the game guidance law is greatly reduced by using the two-step shooting algorithm.

[0038] In the embodiment, the non-external force dynamics refers to the orbit angular velocity n = 0, that is, only the motion of the two spacecrafts in the inertial space under the action of the thruster thrust is considered, without orbit constraint.

[0039] The specific implementation process of establishing the real game optimization model of the two spacecrafts under the external force dynamics in step 100 includes:

[0040] The relative motion model of the tracking spacecraft and the escaping spacecraft is established as:

[0041]

[0042]

[0043] Wherein, x = x p -x e = [x y z v x v y v z ] T is the game state, x p , x e are the state vectors of the tracking spacecraft and the escaping spacecraft in the game coordinate system, respectively, x, y, z are the position coordinates in the x, y, z directions of the game coordinate system, respectively, v x , v y , v z are three components of the tracking spacecraft relative to the escaping spacecraft in the game coordinate system; n is the orbit angular velocity of the game coordinate system running on the reference circular orbit, subscript p refers to the tracker, and subscript e refers to the escapee; the control amount is the thrust acceleration vector, u p = [u px u py u pz ] T , u e = [u ex u ey u ez ] T , and satisfies |up |≤T p 、|u e |≤T e T p and T e These are the maximum accelerations that a tracking spacecraft and an escape spacecraft can generate, respectively.

[0044] Define the pay function for the tracker as follows:

[0045]

[0046] In contrast, for those who evade, the terminal time is the variable to be determined.

[0047] like Figure 4 As shown, the control model for the thrust azimuth and elevation angles is constructed as follows:

[0048]

[0049] Where α is the thrust direction angle, with a value range of [-π, π]; β is the thrust elevation angle, with a value range of a m The thrust acceleration is constant.

[0050] Substituting equation (3) into equation (1), we get:

[0051]

[0052] Where, α p β p These are the thrust azimuth and thrust elevation angles of the tracker, respectively, α e β e These are the thrust azimuth and thrust elevation angles of the escapee, respectively, a p a e These are the constant accelerations of the pursuer and the evader, respectively.

[0053] For the tracker, the desired relative distance and relative velocity of the terminal are both zero, and the terminal condition is x. f =0, assuming the initial game state is x0, then the boundary conditions are:

[0054]

[0055] Among them, T f The terminal time is given by equations (2), (4) and (5). Together, they constitute a real game optimization model for dual-spacecraft survival-type pursuit and capture. This problem is a differential game with free terminal time and fixed terminal state.

[0056] The specific implementation process of establishing the optimal control conditions for the real game optimization model in step 200 includes:

[0057] The Hamilton function of controlling the azimuth of thrust and the high-low angle of thrust is established:

[0058]

[0059] wherein λ = [λ1λ2λ3λ4λ5λ6] T is the adjoint variable;

[0060] The necessary condition of optimal control is:

[0061]

[0062] The extreme condition and the judgment condition of the pursuer are the same as those of the evader, and the optimal control direction angle of the pursuer is the same as that of the evader; the optimal control condition of the real game optimization model is:

[0063]

[0064] In step 300, the optimal solution of the simplified game model of the double space vehicles under the non-external force dynamics is solved by using the modified shooting method based on the optimal control condition, and the optimal control law of the double space vehicles is obtained, which is used as the initial value of the real game problem. The specific implementation process includes:

[0065] First, the simplified game optimization model of the double space vehicles under the non-external force dynamics is established, and the specific implementation process includes:

[0066] ①The adjoint equation

[0067] From the Hamilton function, there is

[0068]

[0069] wherein, λ0= [λ 10 λ 20 λ 30 λ 40 λ 50 λ 60 ] T is the initial value of the adjoint vector;

[0070] The specific form of the adjoint variable related to the control direction angle is:

[0071]

[0072] ②The transversality condition

[0073] The survival type of pursuit and evasion game is an integral type of payment functional, the target set function is the terminal state, and the transversality condition is:

[0074] H(T f ,λ(T f ),x* (T f ),u p * (T f ),u e * (T f ))=0 (11)

[0075] According to the cross-sectional condition (11), Hamilton function (6), boundary condition (5) and optimal control condition (8), we have:

[0076]

[0077] Let a m =a p -a e :

[0078]

[0079] ③Terminal state equation

[0080] Integrate the differential equation (6) of the game state from 0 to t f :

[0081]

[0082] Substitute the optimal control condition (8), the expression of the adjoint variable (10) and the terminal state x0 into the above equation (14):

[0083]

[0084] where,

[0085]

[0086] A = λ 10 2 + λ 20 2 + λ 30 2 ; B = -2(λ 10 λ 40 + λ 20 λ 50 + λ 30 λ 60 ); C = λ 40 2 + λ 50 2 + λ 60 2

[0087] ④Equation group to be solved

[0088] Combining (12) and (15), the original two-point boundary value problem derived from the differential game is transformed into the following nonlinear equations with 7 unknowns λ 10 , λ 20 , λ 30 , λ 40 , λ 50 , λ 60 , t f : (co-state variables and terminal time)

[0089]

[0090] The optimal control condition is input into the simplified game model to construct an optimal control condition for the game problem without external force, and the specific implementation process includes:

[0091]

[0092] The optimal control condition is:

[0093]

[0094] The co-state variables are further constrained by the prior information of the thrust direction at the initial and final boundary positions:

[0095]

[0096] The following relationship is calculated:

[0097] λ 50 = λ 40 tanα0,

[0098] With the above relationship, the 7 co-state variables and the initial value of the terminal time optimization are reduced in dimension to the estimation problem of the co-state variable λ 40 , the terminal time t f and the optimal control direction angle α0, α f , as follows:

[0099] ① Estimate λ 40

[0100]

[0101] λ 40 and cosα0 are opposite in sign, and when there is insufficient information about λ 40 , let:

[0102] λ 40ig = -sign(cosα0) (22)

[0103] The subscript ig represents the initial guess;

[0104] 2. Estimate t f

[0105] As Figure 5 shown, the simplest way to transfer from a state with non-zero initial velocity and position to a zero state is to first uniformly accelerate and then uniformly decelerate, as shown in S' segment, with terminal time t f The estimate of t

[0106]

[0107] 3. Estimate control direction angles a0, a f

[0108] As Figure 6 shown, let r0be the initial position, i v0 be the unit vector of the initial velocity direction, and i e0 be the unit vector from the initial position to the target position. Assuming that the dashed line parallel to i v0 and i e0 divides the plane into four regions with r0as the intersection point, it is derived from the properties of the optimal trajectory that the initial thrust direction should be in region I.

[0109] Let the initial thrust and the terminal thrust be:

[0110] a0= a m (i e0 -k1i v0 ) / |i e0 -k1i v0 | (24)

[0111] a f =-v f- =-a m (i e0 -k2i v0 ) / |i e0 -k2i v0 | (25)

[0112] k1and k2are valued as follows to construct an initial guess that effectively fits the optimal result:

[0113]

[0114] where k p is a proportional coefficient, and a value range of 0.2-0.9 is recommended; k m and Δk m are adjustment coefficients, k m = 4.5 and Δk m = 1;

[0115] Based on the constructed initial and terminal thrust vectors, the direction angle estimates are calculated:

[0116]

[0117] Further, the initial guess construction formula of the time-optimal parking problem under no external force is calculated from formula (22), (23) and (27) combined with formula (20), that is, the optimal control condition of the game problem under no external force:

[0118] a0=a m (i e0 -k1i v0 ) / |i e0 -k1i v0 |

[0119] a f =-a m (i e0 -k2i v0 ) / |i e0 -k2i v0

[0120] α 0ig =arctan(a0(2),a0(1))

[0121] α fig =arctan(a f (2),a f (1))

[0122]

[0123] λ 40ig =-sign(cosα 0ig )

[0124] λ 50ig =λ 40ig tanα 0ig

[0125]

[0126]

[0127] According to the azimuth estimation of the optimal thrust, the specific implementation process of constructing the initial value of the simplified game model includes: the time-optimal trajectory of the game problem under no external force is in a spatial plane, so its initial value is also the initial value of the plane problem as shown in formula (28). Considering the initial value requirement of the three-dimensional game under the real external force environment, the initial value of the three-dimensional game problem under no external force is expanded and calculated according to the initial value of the plane problem under no external force, which is as follows:

[0128] a0=a m (i e0 -k1iv0 ) / i e0 -k1i v0 |

[0129] a f =-a m (i e0 -k2i v0 ) / |i e0 -k2i v0 |

[0130] α 0ig =arctan2(a0(2),a0(1))

[0131] α fig =arctan2(a f (2),a f (1))

[0132]

[0133]

[0134]

[0135] λ 40ig =-sign(cosα 0ig )

[0136] λ 50ig =λ 40ig tanα 0ig

[0137]

[0138]

[0139] According to the initial value of the three-dimensional non-external force dynamics game problem, that is, formula (29), the optimal control law of the three-dimensional game problem of the double space vehicles under the action of no external force is solved by the first shooting through the modified shooting method, and the specific implementation process includes:

[0140] Initialize the given initial guess λ 0ig ; iteration tolerance error e f and equation F to be solved.

[0141] Step 1: Let λ 0,k = λ 0ig .

[0142] Step 2: Let p=1 and calculate the Jacobian matrix

[0143] Step 3: Calculate

[0144] Step 4: Calculate F(λ 0,k ), F(λ 0,k+1 ) and Δ(λ 0,k+1 )

[0145] Step 5: If ||F(λ 0,k+1 )||≤||F(λ 0,k )|| and Δ(λ 0,k+1 )≥0, then go to next step, otherwise let p=p / 2 and go back to step 3.

[0146] Step 6: If ||λ 0,k+1 -λ 0,k ||≤e f , then end iteration and output

[0147] Otherwise let λ 0,k =λ 0,k+1 and go back to step 2.

[0148] The embodiment simplifies the original problem and establishes a simplified optimization problem of two-spacecraft game without considering external force. Based on the qualitative analysis of the optimal trajectory variation characteristics, an initial guess of the simplified problem with good properties is constructed, and then the shooting method is used to solve the simplified problem, and the optimal solution of the game problem under the dynamics without external force is obtained.

[0149] The optimal control law obtained above is used as the initial value of the real game model.

[0150] Based on the initial value of the real game optimization problem obtained in step 300, the optimal solution of the real game optimization model is solved by using the second shooting, and the specific implementation process of the real game guidance law of the double-spacecraft is obtained, including:

[0151] The real game optimization model established in step 100 is solved to obtain the co-state equation, Hamilton function cross-section condition, terminal state equation and equation group of the double-spacecraft real game problem, which are as follows:

[0152] ① Co-state equation

[0153] From the Hamilton function formula, there is

[0154]

[0155] Wherein, is the system matrix of the CW equation;

[0156] The specific expression of the co-state variable related to the control direction angle is:

[0157]

[0158]

[0159]

[0160] ②Crossing condition

[0161] The crossing condition under the CW dynamics is consistent with equation (13);

[0162] ③Terminal state equation

[0163]

[0164] ④Equation group to be solved

[0165] The equation group to be solved under the CW dynamics is obtained by combining the crossing condition and the terminal state equation:

[0166]

[0167] The optimal control law under the non-CW dynamics obtained in step 300 is used as the initial value of the real game optimization model, and the optimal solution of the equation group (32) is obtained by solving the equation group (32) through the second shooting, to obtain the real game guidance law of the double space vehicles, and the specific implementation process includes:

[0168] Initialize the initial states x p0 , x e0 of the given pursuer and evader, and the accelerations a p , a e of both parties Step 1: Let x0 = x p0 -x e0 , a m = a p -a e .

[0169] Step 2: (First shooting) solve the time-optimal parking problem under non-CW dynamics.

[0170] Step 3: Replace F and λ 0ig with and respectively, where the terminal time is also a shooting variable to be solved.

[0171] Step 4: (Second shooting) solve the problem after replacement in step 3 to obtain the initial value of the optimal co-state variable λ0 * and t f * , where the condition Δ(λ 0,k+1 ) ≥ 0 does not need to be considered again.

[0172] Step 5: Substitute λ0 * into the formula to obtain the time function of the optimal control direction angle, i.e. the final control jet direction.

[0173] The beneficial effects of the two-spacecraft game path planning method based on the progressive shooting method of the embodiment are verified using the following examples:

[0174] Suppose the Hill system reference circular orbit height is 600 km, the orbit angular velocity n = 0.001006 rad / s, the initial state of the pursuer relative to the Hill system is x p0 = [5000 6000 3000 -20 50 0] T m, m / s, and the initial state of the evader relative to the Hill system is x e0 = [0 0 0 0 0 50] T m, m / s, the constant acceleration a p of the pursuer is 0.8 m / s 2 , the constant acceleration a e of the evader is 0.3 m / s 2 , the proportional coefficient k p is 0.8, the adjustment coefficient k m is 4.5, and the adjustment coefficient Δk m is 1.

[0175] Through simulation, the iteration tolerance of the first shooting and the second shooting is set to 10 -8 .

[0176] Figure 7 The trajectory results corresponding to the optimal solution and the initial guess are compared, in which the dotted line and the solid line are the results obtained by directly substituting the initial guess λ 0ig and the optimal co-state variable of the first shooting into the optimal control condition (8) and integrating the game state equation (4), respectively, and the branch line segment represents the thrust direction at that position. Figure 7 and Figure 8 respectively show that the corresponding result curves of the optimal solution and the initial guess have similarity in shape and change trend, and the initial guess indeed reflects the characteristics of the optimal solution.

[0177] Figure 9 and Figure 10 are the trajectories and velocities of the pursuer and the evader under the Hill system in the first shooting and the second shooting, respectively. TP-FS and TE-FS represent the trajectories of the pursuer and the evader in the first shooting, respectively; TP-SS and TE-SS represent the trajectories of the pursuer and the evader in the second shooting, respectively. VP-FS, VE-FS, VP-SS, and VE-SS are the corresponding velocities. The velocities of the pursuer and the evader in the second shooting under CW dynamics are complex spatial curves, and the real two-spacecraft game problem has strong nonlinearity. The optimal solution λ 0w * and t fw* As the initial value of the second shooting, the optimal solution λ0 * Very close to λ 0w * The first shooting indeed provides a good initial guess for the real game problem solved by the second shooting.

[0178] The convergence results of the first and second shooting are shown in Figs. Figure 11 , 12 The convergence speed of the second shooting is slower than that of the first shooting in the initial stage due to the strong nonlinearity of the real game problem corresponding to the second shooting. The optimal solution is obtained after 12 iterations in total, i.e., the optimal solution is obtained in only 0.85 s in total.

[0179] The above results show that the progressive shooting method proposed in the present application has good convergence and computational efficiency, and has great advantages in solving the game path planning problem of two spacecrafts, and has potential for practical on-orbit application.

[0180] The serial numbers of the above steps involved in the method of the present application do not mean the order of the execution of the method, and the execution order of the steps should be determined according to the functions and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0181] The above only describes the preferred embodiments of the present application and is not used to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for dual-spacecraft game path planning based on progressive targeting, comprising: establishing a real game optimization model of dual-spacecrafts under external force dynamics; establishing optimal control conditions of the real game optimization model; solving optimal solutions of a simplified game model of dual-spacecrafts under no external force dynamics based on the optimal control conditions by using a modified targeting method; taking the optimal solutions of the simplified game model as initial values of the real game optimization model, and solving optimal solutions of the real game optimization model by using a second targeting to obtain real game guidance laws of dual-spacecrafts; the dual-spacecrafts include a pursuit spacecraft and an evading spacecraft; the real game optimization model of dual-spacecrafts under external force dynamics is established, comprising: establishing a relative motion model of the pursuit spacecraft and the evading spacecraft as: where x = x p -x e = [x y z v x v y v z ] T is the game state, x p , x e are the state vectors of the pursuit spacecraft and the evading spacecraft in the game coordinate system, x, y, z are the position coordinates in the x, y, z directions of the game coordinate system, v x , v y , v z are the three components of the relative speed of the pursuer to the evader in the game coordinate system; n is the orbital angular velocity of the game coordinate system on the reference circular orbit, the subscript p refers to the pursuer, and the subscript e refers to the evader; the control quantity is the thrust acceleration vector, u p = [u px u py u pz ] T , u e = [u ex u ey u ez ] T , and satisfy |u p |≤T p , |u e |≤T e , T p and T e are the maximum accelerations that the pursuit spacecraft and the evading spacecraft can generate, respectively. defining a payoff function of the pursuer as: and the evader is opposite to the pursuer, and a terminal time is a variable to be solved; constructing a control model of a thrust azimuth angle and a thrust elevation angle as: Wherein, a is the thrust direction angle, the value range [-π, π]; β is the thrust high-low angle, the value range a m is the constant thrust acceleration; substituting equation (3) into equation (1) to obtain: where α p , β p are the thrust azimuth and thrust pitch angles of the pursuer, respectively, α e , β e are the thrust azimuth and thrust pitch angles of the evader, respectively, and a p , a e are constant accelerations of the pursuer and the evader, respectively. For the pursuer, the terminal conditions are x f = 0, and the boundary condition is x = x0, assuming the initial game state is x0. where T f is the terminal time; formula (2), formula (4) and formula (5) constitute a real game optimization model of double-spacecraft survival-type pursuit and capture, which is a differential game with free terminal time and fixed terminal state.

2. The method of claim 1, wherein, establishing optimal control conditions of the real game optimization model, comprising: establishing a Hamilton function of the control thrust azimuth angle and the thrust elevation angle: where λ = [λ1 λ2 λ3 λ4 λ5 λ6] T is the coordination variable; a necessary condition for optimal control is: extreme conditions and judgment conditions of the pursuer are the same as those of the evader, and optimal control direction angles of the pursuer and the evader are the same; the optimal control conditions of the real game optimization model are:

3. The method of claim 2, wherein, solving optimal solutions of a simplified game model of dual-spacecrafts under no external force dynamics based on the optimal control conditions by using a modified targeting method, comprising: establishing the simplified game model of dual-spacecrafts under no external force dynamics; inputting the optimal control conditions into the simplified game model to construct optimal control conditions of a game problem under no external force; constructing initial values of the simplified game model according to optimal thrust azimuth estimation, and solving optimal control laws of the game problem of dual-spacecrafts under no external force by using a first targeting by a modified targeting method, and taking the optimal solutions as initial values of the real game optimization model.

4. The method of claim 3, wherein, the optimal control conditions of the game problem under no external force include initial costate variables, a terminal time, and optimal control direction angles.

5. The method of claim 3, wherein, taking the optimal solutions of the simplified game model as initial values of the real game optimization model, and solving optimal solutions of the real game optimization model by using a second targeting to obtain real game guidance laws of dual-spacecrafts, comprising: solving the real game optimization model to obtain a costate equation of the real game problem of dual-spacecrafts, a Hamilton function cross-section condition, a terminal state equation, and an equation group to be solved; taking the optimal control laws as initial values of the equation group to be solved, and solving the optimal solutions of the real game problem by using a second targeting to obtain real game guidance laws of dual-spacecrafts.

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